Measurement-induced nonlocality for an arbitrary bipartite state

Mirafzali, Sayyed Yahya; Sargolzahi, Iman; Ahanj, Ali; Javidan, Kurosh; Sarbishaei, Mohsen

doi:10.26421/qic13.5-6-8

Cited by 6 publications

(6 citation statements)

References 2 publications

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“…Fortunately, several well-defined measures of MIN have been introduced to remedy the problem, such as those based on relative entropy [15], von Neumann entropy [16], trace norm [17], uncertainty [18] and square root [19]. Moreover, the monogamy property [20], the evaluation [21], and the factorization relation of evolution [22] for MIN are also studied extensively.…”

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confidence: 99%

Measurement-induced nonlocality based on Wigner-Yanase skew information

Wang

Shen

et al. 2016

EPL

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Measurement-induced nonlocality (MIN), which describes the maximum global effect caused by locally invariant measurements, was introduced by Luo and Fu (Phys. Rev. Lett., 106 (2011) 120401). In this paper, a new measure of MIN based on Wigner-Yanase skew information is proposed. It is shown that this measure not only has good computability but also eliminates the noncontractivity problem appearing in the original measure of MIN defined by the Hilbert-Schmidt norm. The analytical formulas of MIN based on Wigner-Yanase skew information for any pure states, (2 × n)-dimensional mixed states, and some higher-dimensional symmetric states are presented. Furthermore, the tight upper bound to MIN based on Wigner-Yanase skew information in the general case is also derived.

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confidence: 99%

Measurement-induced nonlocality based on Wigner-Yanase skew information

Wang

Shen

et al. 2016

EPL

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“…This MIN measure can be derived analytically for a wide range of quantum states, which include the pure states, the bipartite states ρ AB with A being a qubit, certain higher dimensional states with symmetry, as well as certain bound entangled states (Rana and Parashar, 2013) and other special states with degenerate ρ A (Mirafzali et al, 2013). Some of the results are summarized as follows:…”

Section: Hilbert-schmidt Norm Of Minmentioning

confidence: 99%

Quantum coherence and geometric quantum discord

Hu,

Wang

et al. 2017

Preprint

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Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics. They are also cornerstones of quantum computation and quantum communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states.We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.

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“…The MIN has been one of current research focuses for years [19][20][21][22][23][24][25][26][27]. However, its quantification based on the Hilbert-Schmidt norm (we call it conventional MIN for brevity), while intuitively appealing and conceptually significant, has certain discouraging properties.…”

Section: Min Quantified By Hilbert-schmidt Normmentioning

confidence: 99%

Measurement-induced nonlocality based on the trace norm

Fan

2015

New J. Phys.

114

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Nonlocality is one unique property of quantum mechanics differing from classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, termed as measurement-induced nonlocality (MIN) (2011 Phys. Rev. Lett. 106 120401). Here, we propose to quantify the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of completely positive trace-preserving map, which is the general local quantum operation, on the unmeasured party for the bipartite state. This property avoids the undesirable characteristic appearing in the known measure of MIN defined by the Hilbert-Schmidt norm that may be increased or decreased by trivial local reversible operations on the unmeasured party. We obtain analytical formulas of the trace-norm MIN for any 2 × n dimensional pure state, two-qubit state, and certain high-dimensional states. As other quantum correlation measures, the new defined MIN can be directly applied to various models for physical interpretations.

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Measurement-induced nonlocality for an arbitrary bipartite state

Cited by 6 publications

References 2 publications

Measurement-induced nonlocality based on Wigner-Yanase skew information

Measurement-induced nonlocality based on Wigner-Yanase skew information

Quantum coherence and geometric quantum discord

Measurement-induced nonlocality based on the trace norm

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